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From: Wei Dai <weidai.domain.name.hidden>

Date: Sun, 10 Jan 1999 15:13:46 -0800

On Mon, Jan 11, 1999 at 09:53:44AM +1100, Russell Standish wrote:

*> It would certainly help to define some terms - what do you
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*> mean by B* (powerset of B? set of all binary strings?) What exactly is
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*> a universal prefix machine? Can it be any map from B* to N?
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As I said, the notation is from Li and Vitanyi. B* is the set of all

finite binary strings. A universal prefix machine is a kind of universal

Turing machine where no program is a prefix of another.

*> > U'(u)(x) = \sum_{U(p)=x}u(p)
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*>
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*> This definition doesn't even parse. U' is defined over the set of
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*> universal prefix machines, not (something) x N. What is u? And what is
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*> the index that the sum is performed over - {p:U(p)=x}, or is it
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*> {U:U(p)=x}? In any case the independent variable ought to appear on
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*> the RHS.
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U' is not defined over the set of universal prefix machines, it's defined

over the set of measures on infinite binary strings. Since I already

specified U is some particular universal prefix machine, the only

available index is p.

*> I think I'd better bail at this point, pending clarification.
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Hope that helps.

Received on Sun Jan 10 1999 - 15:16:25 PST

Date: Sun, 10 Jan 1999 15:13:46 -0800

On Mon, Jan 11, 1999 at 09:53:44AM +1100, Russell Standish wrote:

As I said, the notation is from Li and Vitanyi. B* is the set of all

finite binary strings. A universal prefix machine is a kind of universal

Turing machine where no program is a prefix of another.

U' is not defined over the set of universal prefix machines, it's defined

over the set of measures on infinite binary strings. Since I already

specified U is some particular universal prefix machine, the only

available index is p.

Hope that helps.

Received on Sun Jan 10 1999 - 15:16:25 PST

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